Chef and Pair Flips

Chef has two matrices $A$ and $B$, each with size $N \times M$. Each cell of the matrix $A$ contains a character '0' or '1', while each cell of the matrix $B$ contains '?', '0' or '1'. The matrix $A$ can be modified using zero or more operations. In one operation, Chef can choose two cells in the matrix $A$ which lie either in the same row or in the same column and flip the characters in each o